Here we keep the results of various numerical experiments of optimal control outcomes in the Cholera model. Specifically, we focus on the difference between the optimal strategy, when control is customized to each patch versus the “one size fits all strategy” where both patches are forced to be given the same control.
The following experiments use these parameters and initial conditions.
Parameters:
| mu1 | mu2 | beta_I1 | beta_I2 | beta_W1 | beta_W2 | v1 | v2 | u1 | u2 | m1 | m2 | n1 | n2 | gamma1 | gamma2 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 0 | 2.64e-06 | 2.64e-06 | 1.01e-05 | 1.01e-05 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0.25 | 0.25 |
| delta1 | delta2 | xi1 | xi2 | nu1 | nu2 | rho1 | rho2 |
|---|---|---|---|---|---|---|---|
| 5e-04 | 5e-04 | 0.00756 | 0.00756 | 0.00756 | 0.00756 | 0.025 | 0.025 |
Initial conditions:
| S1 | S2 | I1 | I2 | R1 | R2 | W1 | W2 |
|---|---|---|---|---|---|---|---|
| 92791 | 94406 | 1609 | 1440 | 5589 | 4145 | 118 | 120 |
Optimal control parameters:
| b1 | b2 | C1 | C2 | epsilon1 | epsilon2 | D1 | D2 | eta1 | eta2 | tol | control_type |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 1 | 0.125 | 0.125 | 10000 | 10000 | 0.0125 | 0.0125 | 1000 | 1000 | 0.01 | unique |
| v1_min | v1_max | v2_min | v2_max | u1_min | u1_max | u2_min | u2_max |
|---|---|---|---|---|---|---|---|
| 0 | 0.015 | 0 | 0.015 | 0 | 0.4 | 0 | 0.4 |
With these parameters, the system has an R0 of about 1.9898893.
Time 0 corresponds to 100 days since the start of the outbreak.
We consider the case with only vaccination (no sanitation).
Controls start at day 100.
We also consider the case with only sanitation (no vaccination).
Controls start at day 100`.
Lastly, we show how results change if we optimize both controls.
Controls start at day 100.
The following experiments use these parameters and initial conditions.
Parameters:
| mu1 | mu2 | beta_I1 | beta_I2 | beta_W1 | beta_W2 | v1 | v2 | u1 | u2 | m1 | m2 | n1 | n2 | gamma1 | gamma2 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 0 | 2.6e-06 | 2.6e-06 | 1.01e-05 | 1.01e-05 | 0 | 0 | 0 | 0 | 0.05 | 0.05 | 0 | 0 | 0.25 | 0.25 |
| delta1 | delta2 | xi1 | xi2 | nu1 | nu2 | rho1 | rho2 |
|---|---|---|---|---|---|---|---|
| 5e-04 | 5e-04 | 0.00756 | 0.00756 | 0.00756 | 0.00756 | 0.025 | 0.025 |
Initial conditions: need to re-calculate initial conditions with movement
| S1 | S2 | I1 | I2 | R1 | R2 | W1 | W2 |
|---|---|---|---|---|---|---|---|
| 92791 | 94406 | 1609 | 1440 | 5589 | 4145 | 118 | 120 |
Optimal control parameters:
| b1 | b2 | C1 | C2 | epsilon1 | epsilon2 | D1 | D2 | eta1 | eta2 | tol | control_type |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 1 | 0.125 | 0.125 | 10000 | 10000 | 0.0125 | 0.0125 | 1000 | 1000 | 0.01 | unique |
| v1_min | v1_max | v2_min | v2_max | u1_min | u1_max | u2_min | u2_max |
|---|---|---|---|---|---|---|---|
| 0 | 0.015 | 0 | 0.015 | 0 | 0.4 | 0 | 0.4 |
With these parameters, the system has an R0 of about 1.9898893.
Time 0 corresponds to 100 days since the start of the outbreak. This is currently incorrect. It’s not taking into account movement
We consider the case with only vaccination (no sanitation).
Controls start at day 100.
We also consider the case with only sanitation (no vaccination).
Controls start at day 100`.
Lastly, we show how results change if we optimize both controls.
Controls start at day 100.
The following experiments use these parameters and initial conditions.
Parameters:
| mu1 | mu2 | beta_I1 | beta_I2 | beta_W1 | beta_W2 | v1 | v2 | u1 | u2 | m1 | m2 | n1 | n2 | gamma1 | gamma2 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 0 | 2.6e-06 | 2.6e-06 | 1.01e-05 | 1.01e-05 | 0 | 0 | 0 | 0 | 0.1 | 0.1 | 0 | 0 | 0.25 | 0.25 |
| delta1 | delta2 | xi1 | xi2 | nu1 | nu2 | rho1 | rho2 |
|---|---|---|---|---|---|---|---|
| 5e-04 | 5e-04 | 0.00756 | 0.00756 | 0.00756 | 0.00756 | 0.025 | 0.025 |
Initial conditions: need to re-calculate initial conditions with movement
| S1 | S2 | I1 | I2 | R1 | R2 | W1 | W2 |
|---|---|---|---|---|---|---|---|
| 92791 | 94406 | 1609 | 1440 | 5589 | 4145 | 118 | 120 |
Optimal control parameters:
| b1 | b2 | C1 | C2 | epsilon1 | epsilon2 | D1 | D2 | eta1 | eta2 | tol | control_type |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 1 | 0.125 | 0.125 | 10000 | 10000 | 0.0125 | 0.0125 | 1000 | 1000 | 0.01 | unique |
| v1_min | v1_max | v2_min | v2_max | u1_min | u1_max | u2_min | u2_max |
|---|---|---|---|---|---|---|---|
| 0 | 0.015 | 0 | 0.015 | 0 | 0.4 | 0 | 0.4 |
With these parameters, the system has an R0 of about 1.9898893.
Time 0 corresponds to 100 days since the start of the outbreak. This is currently incorrect. It’s not taking into account movement
We consider the case with only vaccination (no sanitation).
Controls start at day 100.
We also consider the case with only sanitation (no vaccination).
Controls start at day 100`.
Lastly, we show how results change if we optimize both controls.
Controls start at day 100.
The following experiments use these parameters and initial conditions.
Parameters:
| mu1 | mu2 | beta_I1 | beta_I2 | beta_W1 | beta_W2 | v1 | v2 | u1 | u2 | m1 | m2 | n1 | n2 | gamma1 | gamma2 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 0 | 2.6e-06 | 2.6e-06 | 1.01e-05 | 1.01e-05 | 0 | 0 | 0 | 0 | 0.05 | 0.1 | 0 | 0 | 0.25 | 0.25 |
| delta1 | delta2 | xi1 | xi2 | nu1 | nu2 | rho1 | rho2 |
|---|---|---|---|---|---|---|---|
| 5e-04 | 5e-04 | 0.00756 | 0.00756 | 0.00756 | 0.00756 | 0.025 | 0.025 |
Initial conditions: need to re-calculate initial conditions with movement
| S1 | S2 | I1 | I2 | R1 | R2 | W1 | W2 |
|---|---|---|---|---|---|---|---|
| 92791 | 94406 | 1609 | 1440 | 5589 | 4145 | 118 | 120 |
Optimal control parameters:
| b1 | b2 | C1 | C2 | epsilon1 | epsilon2 | D1 | D2 | eta1 | eta2 | tol | control_type |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 1 | 0.125 | 0.125 | 10000 | 10000 | 0.0125 | 0.0125 | 1000 | 1000 | 0.01 | unique |
| v1_min | v1_max | v2_min | v2_max | u1_min | u1_max | u2_min | u2_max |
|---|---|---|---|---|---|---|---|
| 0 | 0.015 | 0 | 0.015 | 0 | 0.4 | 0 | 0.4 |
With these parameters, the system has an R0 of about 1.9898893.
Time 0 corresponds to 100 days since the start of the outbreak. This is currently incorrect. It’s not taking into account movement
We consider the case with only vaccination (no sanitation).
Controls start at day 100.
We also consider the case with only sanitation (no vaccination).
Controls start at day 100`.
Lastly, we show how results change if we optimize both controls.
Controls start at day 100.
The following experiments use these parameters and initial conditions.
Parameters:
| mu1 | mu2 | beta_I1 | beta_I2 | beta_W1 | beta_W2 | v1 | v2 | u1 | u2 | m1 | m2 | n1 | n2 | gamma1 | gamma2 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 0 | 2.6e-06 | 2.6e-06 | 1.01e-05 | 1.01e-05 | 0 | 0 | 0 | 0 | 0.05 | 0.1 | 0 | 0 | 0.25 | 0.25 |
| delta1 | delta2 | xi1 | xi2 | nu1 | nu2 | rho1 | rho2 |
|---|---|---|---|---|---|---|---|
| 5e-04 | 5e-04 | 0.00756 | 0.00756 | 0.00756 | 0.00756 | 0.025 | 0.025 |
Initial conditions: need to re-calculate initial conditions with movement
| S1 | S2 | I1 | I2 | R1 | R2 | W1 | W2 |
|---|---|---|---|---|---|---|---|
| 92791 | 94406 | 1609 | 1440 | 5589 | 4145 | 118 | 120 |
Optimal control parameters:
| b1 | b2 | C1 | C2 | epsilon1 | epsilon2 | D1 | D2 | eta1 | eta2 | tol | control_type |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 1 | 0.125 | 0.125 | 10000 | 10000 | 0.0125 | 0.0125 | 1000 | 1000 | 0.01 | unique |
| v1_min | v1_max | v2_min | v2_max | u1_min | u1_max | u2_min | u2_max |
|---|---|---|---|---|---|---|---|
| 0 | 0.015 | 0 | 0.015 | 0 | 0.4 | 0 | 0.4 |
With these parameters, the system has an R0 of about 1.9898893.
Time 0 corresponds to 100 days since the start of the outbreak. This is currently incorrect. It’s not taking into account movement
We consider the case with only vaccination (no sanitation).
Controls start at day 100.
We also consider the case with only sanitation (no vaccination).
Controls start at day 100`.
Lastly, we show how results change if we optimize both controls.
Controls start at day 100.
We show similar results instead employing the Ebola model.
The following experiments use these parameters and initial conditions.
Parameters:
| mu1 | alpha1 | gammaI1 | gammaH1 | phi1 | deltaI1 | deltaH1 | xi1 | m1 | n1 |
|---|---|---|---|---|---|---|---|---|---|
| 5.5e-05 | 0.1 | 0.0666667 | 0.028 | 0.236 | 0.024 | 0.01 | 0.222 | 1e-05 | 0 |
| mu2 | alpha2 | gammaI2 | gammaH2 | phi2 | deltaI2 | deltaH2 | xi2 | m2 | n2 |
|---|---|---|---|---|---|---|---|---|---|
| 5.5e-05 | 0.1 | 0.0666667 | 0.028 | 0.236 | 0.024 | 0.01 | 0.222 | 0.001 | 0 |
Initial conditions:
| S1 | E1 | I1 | H1 | D1 | R1 | S2 | E2 | I2 | H2 | D2 | R2 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 99300 | 400 | 300 | 0 | 0 | 0 | 1e+05 | 0 | 0 | 0 | 0 | 0 |
Optimal control parameters:
| b1 | b2 | C1 | C2 | epsilon1 | epsilon2 | control_type | tol | v1 | v2 |
|---|---|---|---|---|---|---|---|---|---|
| 1 | 1 | 0.01 | 0.01 | 50000 | 50000 | uniform | 0.01 | 0 | 0 |
| v1_min | v1_max | v2_min | v2_max | betaI1 | betaI2 | betaD1 | betaD2 | N1 | N2 |
|---|---|---|---|---|---|---|---|---|---|
| 0 | 0.015 | 0 | 0.015 | 1e-07 | 1e-07 | 5.94e-05 | 5.94e-05 | 1e+05 | 1e+05 |
Need to add Ebola R0 calculation
Time 0 corresponds to 100 days since the start of the outbreak. This is currently incorrect. It’s not taking into account movement
We consider the case with only vaccination (no TBD).
Controls start at day 100.
We also consider the case with only TBD (no vaccination).
Controls start at day 100`.
Lastly, we show how results change if we optimize both controls.
Controls start at day 100.
The following experiments use these parameters and initial conditions.
Parameters:
| mu1 | alpha1 | gammaI1 | gammaH1 | phi1 | deltaI1 | deltaH1 | xi1 | m1 | n1 |
|---|---|---|---|---|---|---|---|---|---|
| 5.5e-05 | 0.1 | 0.0666667 | 0.028 | 0.236 | 0.024 | 0.01 | 0.222 | 1e-05 | 0 |
| mu2 | alpha2 | gammaI2 | gammaH2 | phi2 | deltaI2 | deltaH2 | xi2 | m2 | n2 |
|---|---|---|---|---|---|---|---|---|---|
| 5.5e-05 | 0.1 | 0.0666667 | 0.028 | 0.236 | 0.024 | 0.01 | 0.222 | 0.001 | 0 |
Initial conditions:
| S1 | E1 | I1 | H1 | D1 | R1 | S2 | E2 | I2 | H2 | D2 | R2 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 99300 | 400 | 300 | 0 | 0 | 0 | 1e+05 | 0 | 0 | 0 | 0 | 0 |
Optimal control parameters:
| b1 | b2 | C1 | C2 | epsilon1 | epsilon2 | control_type | tol | v1 | v2 |
|---|---|---|---|---|---|---|---|---|---|
| 1 | 1 | 0.01 | 0.01 | 50000 | 50000 | uniform | 0.01 | 0 | 0 |
| v1_min | v1_max | v2_min | v2_max | betaI1 | betaI2 | betaD1 | betaD2 | N1 | N2 |
|---|---|---|---|---|---|---|---|---|---|
| 0 | 0.015 | 0 | 0.015 | 1e-07 | 1e-07 | 5.94e-05 | 5.94e-05 | 1e+05 | 1e+05 |
Need to add Ebola R0 calculation
Time 0 corresponds to 100 days since the start of the outbreak. This is currently incorrect. It’s not taking into account movement
We consider the case with only vaccination (no TBD).
Controls start at day 100.
We also consider the case with only TBD (no vaccination).
Controls start at day 100`.
Lastly, we show how results change if we optimize both controls.
Controls start at day 100.
The following experiments use these parameters and initial conditions.
Parameters:
| mu1 | alpha1 | gammaI1 | gammaH1 | phi1 | deltaI1 | deltaH1 | xi1 | m1 | n1 |
|---|---|---|---|---|---|---|---|---|---|
| 5.5e-05 | 0.1 | 0.0666667 | 0.028 | 0.236 | 0.024 | 0.01 | 0.222 | 1e-05 | 0 |
| mu2 | alpha2 | gammaI2 | gammaH2 | phi2 | deltaI2 | deltaH2 | xi2 | m2 | n2 |
|---|---|---|---|---|---|---|---|---|---|
| 5.5e-05 | 0.1 | 0.0666667 | 0.028 | 0.236 | 0.024 | 0.01 | 0.222 | 0.001 | 0 |
Initial conditions:
| S1 | E1 | I1 | H1 | D1 | R1 | S2 | E2 | I2 | H2 | D2 | R2 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 99300 | 400 | 300 | 0 | 0 | 0 | 1e+05 | 0 | 0 | 0 | 0 | 0 |
Optimal control parameters:
| b1 | b2 | C1 | C2 | epsilon1 | epsilon2 | control_type | tol | v1 | v2 |
|---|---|---|---|---|---|---|---|---|---|
| 1 | 1 | 0.01 | 0.01 | 50000 | 50000 | uniform | 0.01 | 0 | 0 |
| v1_min | v1_max | v2_min | v2_max | betaI1 | betaI2 | betaD1 | betaD2 | N1 | N2 |
|---|---|---|---|---|---|---|---|---|---|
| 0 | 0.015 | 0 | 0.015 | 1e-07 | 1e-07 | 5.94e-05 | 5.94e-05 | 1e+05 | 1e+05 |
Need to add Ebola R0 calculation
Time 0 corresponds to 100 days since the start of the outbreak. This is currently incorrect. It’s not taking into account movement
We consider the case with only vaccination (no TBD).
Controls start at day 100.
We also consider the case with only TBD (no vaccination).
Controls start at day 100`.
Lastly, we show how results change if we optimize both controls.
Controls start at day 100.
The following experiments use these parameters and initial conditions.
Parameters:
| mu1 | alpha1 | gammaI1 | gammaH1 | phi1 | deltaI1 | deltaH1 | xi1 | m1 | n1 |
|---|---|---|---|---|---|---|---|---|---|
| 5.5e-05 | 0.1 | 0.0666667 | 0.028 | 0.236 | 0.024 | 0.01 | 0.222 | 1e-05 | 0 |
| mu2 | alpha2 | gammaI2 | gammaH2 | phi2 | deltaI2 | deltaH2 | xi2 | m2 | n2 |
|---|---|---|---|---|---|---|---|---|---|
| 5.5e-05 | 0.1 | 0.0666667 | 0.028 | 0.236 | 0.024 | 0.01 | 0.222 | 0.001 | 0 |
Initial conditions:
| S1 | E1 | I1 | H1 | D1 | R1 | S2 | E2 | I2 | H2 | D2 | R2 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 99300 | 400 | 300 | 0 | 0 | 0 | 1e+05 | 0 | 0 | 0 | 0 | 0 |
Optimal control parameters:
| b1 | b2 | C1 | C2 | epsilon1 | epsilon2 | control_type | tol | v1 | v2 |
|---|---|---|---|---|---|---|---|---|---|
| 1 | 1 | 0.01 | 0.01 | 50000 | 50000 | uniform | 0.01 | 0 | 0 |
| v1_min | v1_max | v2_min | v2_max | betaI1 | betaI2 | betaD1 | betaD2 | N1 | N2 |
|---|---|---|---|---|---|---|---|---|---|
| 0 | 0.015 | 0 | 0.015 | 1e-07 | 1e-07 | 5.94e-05 | 5.94e-05 | 1e+05 | 1e+05 |
Need to add Ebola R0 calculation
Time 0 corresponds to 100 days since the start of the outbreak. This is currently incorrect. It’s not taking into account movement
We consider the case with only vaccination (no TBD).
Controls start at day 100.
We also consider the case with only TBD (no vaccination).
Controls start at day 100`.
Lastly, we show how results change if we optimize both controls.
Controls start at day 100.
The following experiments use these parameters and initial conditions.
Parameters:
| mu1 | alpha1 | gammaI1 | gammaH1 | phi1 | deltaI1 | deltaH1 | xi1 | m1 | n1 |
|---|---|---|---|---|---|---|---|---|---|
| 5.5e-05 | 0.1 | 0.0666667 | 0.028 | 0.236 | 0.024 | 0.01 | 0.222 | 1e-05 | 0 |
| mu2 | alpha2 | gammaI2 | gammaH2 | phi2 | deltaI2 | deltaH2 | xi2 | m2 | n2 |
|---|---|---|---|---|---|---|---|---|---|
| 5.5e-05 | 0.1 | 0.0666667 | 0.028 | 0.236 | 0.024 | 0.01 | 0.222 | 0.001 | 0 |
Initial conditions:
| S1 | E1 | I1 | H1 | D1 | R1 | S2 | E2 | I2 | H2 | D2 | R2 |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 99300 | 400 | 300 | 0 | 0 | 0 | 1e+05 | 0 | 0 | 0 | 0 | 0 |
Optimal control parameters:
| b1 | b2 | C1 | C2 | epsilon1 | epsilon2 | control_type | tol | v1 | v2 |
|---|---|---|---|---|---|---|---|---|---|
| 1 | 1 | 0.01 | 0.01 | 50000 | 50000 | uniform | 0.01 | 0 | 0 |
| v1_min | v1_max | v2_min | v2_max | betaI1 | betaI2 | betaD1 | betaD2 | N1 | N2 |
|---|---|---|---|---|---|---|---|---|---|
| 0 | 0.015 | 0 | 0.015 | 1e-07 | 1e-07 | 5.94e-05 | 5.94e-05 | 1e+05 | 1e+05 |
Need to add Ebola R0 calculation
Time 0 corresponds to 100 days since the start of the outbreak. This is currently incorrect. It’s not taking into account movement
We consider the case with only vaccination (no TBD).
Controls start at day 100.
We also consider the case with only TBD (no vaccination).
Controls start at day 100`.
Lastly, we show how results change if we optimize both controls.
Controls start at day 100.